April 1, 1998
Pesin Authors Mathematics Book
Yakov B. Pesin, professor of mathematics and a member of the Penn State Center for Dynamical Systems, has written a book titled Dimension Theory in Dynamical Systems, Contemporary Views and Applications, published by the University of Chicago Press.
The book introduces a new area of research that lies at the interface between dimension theory and the theory of dynamical systems. Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current research, and describes the most important accomplishments of the field. He emphasizes the general concept of characteristics of dimension type and the "dimension" approach to the theory of dynamical systems.
Topics include the dimension interpretation of some well-known invariants of dynamical systems, such as topological and measure-theoretic entropies; mathematical analysis of dimensions that are most often used in applied research, such as correlation and information dimensions; and mathematical theory of invariant multifractals.
"Throughout the book are numerous remarks that contain material aside from the mainstream of the book that provide useful information," Pesin explains. "Also, there are five appendices that briefly survey topics that are closely related to the book chapters and help extend the reader's knowledge."
Pesin's new book is accessible to advanced mathematicians and a wide range of scientists who depend upon mathematical modeling of dynamical processes.
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